197 
these constants are correlated respectively with the inter- 
planetary spaces, and the elementary condensations. 
5. Each of the atomic weights, after the third in the 
groups, is an arithmetical mean of any pair of atomic weights 
at the same distance above and below it ; and the distance 
of each member of the solar system (minus the constant 4) 
is a mean proportional of the distances of any two members, 
externally and internally to it, from the central body. 
6. The geometric ratio of the planetary distances from 
each other terminates at the two members nearest the cen- 
tral body, and approaches to an arithmetical one; and a 
similar departure is also noticeable from the regular arith- 
metical series of the atomic weights of the first two 
members of the groups, which renders the third less than 
an arithmetical mean of the atomic weights of the second 
and fourth members. 
While most of the atomic weights in tables II. III., exclud- 
ing fractions, agree with those generally received by chemists, 
the remainder, except Caesium = 133, do not vary more 
than a unit from the classical numbers. When it is con- 
sidered that some of these numbers have been obtained by 
doubling the fractions of the old atomic weights, and that 
slight differences in the determinations may arise from the 
latent affinity which some elements have for minute quan- 
tities of another, the numbers in the tables are remarkably 
near to those determined by experiment — more so, in fact, 
than is Bode’s law to the actual distances of the planets 
from the sun. 
It will be observed that there are gaps to be occupied by 
two elements in the first group, with atomic weights 154 
and 177, and by their homologues of position in the second 
group, with atomic weights 160 and 184, which remain to 
be discovered. 
The numerical relations subsisting among the atomic 
weights in tables II. III., and their resemblance to the homo- 
